The scaling of the X-ray variability with black hole mass in active galactic nuclei

The relation between the 2-10 keV, long-term, excess variance and active galactic nuclei (AGN) black hole mass is considered in this work. A significant anticorrelation is found between these two quantities in the sense that the excess variance decreases with increasing black hole mass. This anticorrelation is consistent with the hypothesis that the 2-10 keV power spectrum in AGN follows a power law of slope 2 at high frequencies. It then flattens to a slope of 1 below a break frequency, nu(hfb), until a second break frequency, nu(lfb), below which it flattens to a slope of 0. The ratio nu(hfb)/nu(lfb) is equal to 10-30, similar to the ratio of the respective frequencies in Cyg X-1. The power spectrum amplitude in the (frequency x power) space does not depend on black hole mass. Instead, it is roughly equal to 0.02 in all objects. The high-frequency break decreases with increasing black hole mass according to the relation nu(hfb) = 1.5 x 10(-6) /(M/10(7) M-circle dot) Hz, in the case of 'classical' Seyfert 1 galaxies. The excess variance of NGC 4051, a narrow-line Seyfert 1 object, is larger than is expected for its black hole mass and X-ray luminosity. This can be explained if its nu(hfb) is 20 times larger than the value expected in the case of a 'classical' Seyfert 1 with the same black hole mass. Finally, the excess variance versus X-ray luminosity correlation is a by-product of the excess variance versus black hole mass correlation, with AGN accreting at 0.1-0.15 times the Eddington limit. These results are consistent with recent results from the power spectral analysis of AGN. However, as they are based on data from a few objects only, further investigation is necessary to confirm that there is indeed a 'universal' power spectrum shape in AGN (in the sense that the value of the power spectrum parameters of most AGN will be distributed around the 'canonical' slope, and amplitude values listed above). One way to achieve this is to determine the excess variance versus black hole relation more accurately, using data from many more objects. This will be possible in the near future, because it is easier to measure the excess variance of archival light curves than to estimate their power spectrum. The excess variance versus black hole relation can therefore play an important role in the study of the X- ray variability scaling with black hole mass in AGN.